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Study Guide: Statistics Chapter 4, Sections 1-3 (Probability)
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SHORT ANSWER.
1) What is the defini.on of sample space?
2) What is the difference between classical probability, empirical probability and subjec.ve
probability?
3) If a sportscaster makes an educated guess as to how well a team will do this season, he is using
what type of probability?
4) A child gets 20 heads out of 30 tosses of a coin. If he declared the chance of getting a head with
that coin were 2/3, that would be an example of
probability.
5) Nanette must pass through three doors as she walks from her company's foyer to her office. Each
of these doors may be locked or unlocked.
Let A be the event that all three doors are in the same condition. List the outcomes of A. [Let
"L" designate "locked" and U" designate "unlocked".]
6) Nanette must pass through three doors as she walks from her company's foyer to her office. Each
of these doors may be locked or unlocked.
Let C be the event that at least two doors are in the same condition. List the outcomes of C.
[Let "L" designate "locked" and U" designate "unlocked".]
7) If two dice are rolled one time, find the probability of getting a sum less than 5.
8) If a red suit is drawn from an ordinary deck of cards, what is the probability that the card is a
diamond?
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9) A 12-sided die can be made from a geometric solid called a
dodecahedron. Assume that a fair dodecahedron is rolled.
The sample space is {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}.
Find P(Less than 3).
10) For this year's mayoral election, voter dissatisfaction is very high. In a survey of 900 likely voters,
387 said they planned to write in an independent candidate rather than vote for the Democrat or
Republican candidate for mayor.
Estimate the percentage of voters who plan to write in an independent candidate?
11) In a poll of 497 university students, 248 said that they were opposed to legalizing marijuana.
Estimate the percentage of students who oppose legalizing marijuana.
12) A section of an exam contains two multiple-choice questions, each with three answer choices
(listed "A", "B", and "C"). List all the outcomes of the sample space.
13) A section of an exam contains two multiple-choice questions, each with three answer choices
(listed "A", "B", and "C"). Assuming the outcomes to be equally likely, find the probability (as a
reduced fraction) that at least one answer is "A". [Hint: List all the outcomes of the sample space
first.]
14) A section of an exam contains two multiple-choice questions, each with three answer choices
(listed "A", "B", and "C"). Assuming the outcomes to be equally likely, find the probability (as a
reduced fraction) that neither of the answers is "B". [Hint: List all the outcomes of the sample
space first.]
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15) A coin is tossed 589 times and comes up heads 265 times. Use the Empirical Method to
approximate the probability that the coin comes up heads.
16) So far this season, the university's football team has executed 140 running plays, 146 passing
plays, and 18 "trick" plays. What is the probability that the team will not execute a trick play?
17) A Karate club consists of 34 persons holding a black belt (highest rating), 60 persons holding a
brown belt (middle rating), and 87 persons holding a purple belt (lowest rating). What is the
probability that a randomly-selected club member holds a black belt?
18) At a certain college, there were 700 science majors, 300 engineering majors, and 600 business
majors. If one student was selected at random, the probability that the student is an engineering
major is
19) A Karate club consists of 45 persons holding a black belt (highest rating), 64 persons holding a
brown belt (middle rating), and 86 persons holding a purple belt (lowest rating). What is the
probability that a randomly-selected club member holds a brown belt or a purple belt?
20) A jar contains four white marbles, five red marbles, and six black marbles. If a marble were
selected at random, what is the probability that it is white or black?
21) In a fish tank, there are 15 goldfish, 8 angelfish, and 18 guppies. If a fish is selected at random,
find the probability that it is an angelfish or a guppy.
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22) A survey asked respondents to indicate their level of satisfaction with government spending.
The results are show below.
Response
Very satisfied
Somewhat satisfied
Dissatisfied
Total
Number
600
3204
7105
10,909
Assume this is a simple random sample from a population. Use the Empirical Method to estimate
the probability that a person is dissatisfied with government's spending?
23) A survey asked 33,592 homeowners how many pets they owned. The results were as followed:
Number of Pets
0
1
2
3
4 or more
Total
Number of Homeowners
5271
11,960
8877
6071
1413
33,592
Assume this is a simple random sample of homeowners. Use the Empirical Method to
estimate the probability that a homeowner has at least one pet.
24) There are 27,564 undergraduate students enrolled at a certain university. The age distribution
is as follows:
Age Range Number
13 - 14
3
15 - 17
436
18 - 22
11,514
23 - 30
9389
31 and up
6222
Total
27,564
What is the probability that a student is less than 18 years old?
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25) An apartment building has the following distribution of apartments:
1 bedroom
2 bedroom
3 bedroom
1st floor 3
2
1
2nd floor 1
3
2
3rd floor 1
4
1
If an apartment is selected at random, what is the probability that it is not a 2 bedroom apartment
on the 2nd floor?
26) The Statistics Club at Woodvale College sold college T-shirts as a fundraiser. The results of the
sale are shown below. Choose one student at random. Find the probability that the student sold
11-15 T-shirts or less than 6 T-shirts.
No. of t-shirts
0
1-5
6-10
11-15
16-20
20+
No. of club members
1
15
13
4
5
1
27) Let E be the event that a corn crop has an infestation of ear worms, and let B be the event that a
corn crop has an infestation of corn borers.
Suppose that P(E) = 0.19, P(B) = 0.11, and P(E and B) = 0.11. Find the probability that a corn crop
has no corn borer infestation.
28) On a recent Saturday, a total of 1064 people visited a local library. Of these people, 250 were
under age 10, 478 were aged 10–18, 163 were aged 19–30, and the rest were more than 30 years
old.
One person is sampled at random. What is the probability that the person is less than 19 years old?
5
29) On a recent Saturday, a total of 1065 people visited a local library. Of these people, 234 were
under age 10, 489 were aged 10–18, 180 were aged 19–30, and the rest were more than 30 years
old.
One person is sampled at random. What is the probability that the person is more than 30 years
old?
30) In a recent semester at a local university, 480 students enrolled in both General Chemistry and
Calculus I. Of these students, 71 received an A in general chemistry, 57 received an A in calculus,
and 34 received an A in both general chemistry and calculus.
Find the probability that a randomly chosen student did not receive an A in general chemistry.
31) On a certain day, a cheese packaging facility packaged 510 units of mozzarella cheese. Some
of these packages had major flaws, some had minor flaws, and some had both major and
minor flaws. The following table presents the results.
Major Flaw
No Major Flaw
Minor Flaw No Minor Flaw
23
38
75
374
Find the probability that randomly chosen cheese package has no major flaw.
32) If P(A) = 0.4, P(B) = 0.25, and A and B are mutually exclusive, find P(A or B).
33) Let A and B be events with P(A) = 0.8, P(B) = 0.7, and P(B|A) = 0.5. Find P(A and B).
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34) A poll was taken of 14,681 working adults aged 40-70 to determine their level of education. The
participants were classified by sex and by level of education. The results were as follows.
Education Level
High School or Less
Bachelor's Degree
Master's Degree
Ph.D.
Total
Male
3781
3615
585
57
8038
Female
2386
3715
497
45
6643
Total
6167
7330
1082
102
14,681
A person is selected at random. Compute the probability that the person is female and has a
bachelor's degree.
35) A poll was taken of 14,437 working adults aged 40-70 to determine their level of education. The
participants were classified by sex and by level of education. The results were as follows.
Education Level
High School or Less
Bachelor's Degree
Master's Degree
Ph.D.
Total
Male
3448
3042
528
71
7089
Female
2550
4304
451
43
7348
Total
5998
7346
979
114
14,437
A person is selected at random. Compute the probability that the person is male or has a Ph.D.
36) Let A and B be events with P(A) = 0.3, P(B) = 0.8. Assume that A and B are independent. Find
P(A and B).
37) Let A and B be events with P(A) = 0.6, P(B) = 0.4, and P(A and B) = 0.24. Are A and B
independent?
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38) A fair die is rolled five times. What is the probability that it comes up 5 at least once?
39) A fast-food restaurant chain has 643 outlets in the United States. The following table categorizes
them by city population and location and presents the number of outlets in each category. An outlet
is chosen at random from the 643 to test market a new menu.
Region
Population
of city
Under 50,000
50,000 - 500,000
Over 500,000
NE
30
59
77
SE
33
50
126
SW NW
25
23
58
45
73
44
Given that the outlet is located in a city with a population under 50,000, what is the
probability that it is in the Southwest?
40) A lot of 1000 components contains 300 that are defective. Two components are drawn at random
and tested. Let A be the event that the first component drawn is defective, and let B be the event
that the second component drawn is defective.
Find P(B|A).
41) A lot of 1000 components contains 350 that are defective. Two components are drawn at random
and tested. Let A be the event that the first component drawn is defective, and let B be the event
that the second component drawn is defective.
Find P(A).
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42) According to popular belief, 80% of adults enjoy drinking beer. Choose a group of 2 adults at
random. The probability that all of them enjoy drinking beer is:
43) Urn 1 contains 2 red balls and 6 black balls. Urn 2 contains 3 red balls and 5 black balls. Urn 3
contains 5 red balls and 2 black balls. If an urn is selected at random and a ball is drawn, find the
probability it will be red.
44) A group of 12 male and 4 female students is talking about going out for pizza. If 50% of the male
students actually go and 25% of the female students actually go, find the probability that a random
student who goes out for pizza is female.
45) There are 2 first grade children, 4 second grade children, and 7 third grade children in a room.
When choosing two children, what is the conditional probability of choosing a second grade child,
given that either a first or a third grade child was chosen first?
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Answer Key
Testname: STUDY GUIDE CH 4 SEC 1_3
1)
2)
3) subjective probability
4) empirical
5) {LLL, UUU}
6) {LLL, LLU, LUL, LUU,
ULL, ULU, UUL, UUU}
1
7)
6
1
2
9) 1/6
10) 43%
11) 49.9%
12) {AA, AB, AC, BA, BB, BC, CA, CB, CC}
13) 5/9
14) 4/9
15) 0.45
16) 0.941
17) 0.188
3
18)
16
19) 0.769
20) 2/3
26
21)
41
22) 0.651
23) 0.843
24) 0.0159
5
25)
6
26) 0.5128
27) 0.89
28) 0.684
29) 0.152
30) 0.852
31) 0.88
32) 0.65
33) 0.4
34) 0.253
35) 0.494
36) 0.24
37) Yes
38) 0.5981
8)
10
Answer Key
Testname: STUDY GUIDE CH 4 SEC 1_3
39) 0.225
40) 0.2993
41) 0.35
42) 0.640
43)
25
56
44)
1
7
45)
1
3
11